Problem: Given $ m \angle RPS = 8x - 33$, and $ m \angle QPR = 9x + 94$, find $m\angle RPS$. $P$ $Q$ $S$ $R$
From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Since $\angle QPS$ is a straight angle, we know ${m\angle QPS = 180}$ Substitute in the expressions that were given for each measure: $ {9x + 94} + {8x - 33} = {180}$ Combine like terms: $ 17x + 61 = 180$ Subtract $61$ from both sides: $ 17x = 119$ Divide both sides by $17$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $m\angle RPS$ $ m\angle RPS = 8({7}) - 33$ Simplify: $ {m\angle RPS = 56 - 33}$ So ${m\angle RPS = 23}$.